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Cohomologies and deformations of right-symmetric algebras

Askar Dzhumadil'daev
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Abstract

An algebra $A$ with identity $(a\circ b)\circ c-a\circ(b\circ c)=(a\circ c)\circ b-a\circ(c\circ b),$ is called right-symmetric. Cohomology and deformation theory for right-symmetric algebras are developed. Cohomologies of $gl_n$ and half-Witt algebras $W_n^{rsym}, p=0,$ $W_n^{rsym}({\bf m}), p>0,$ are calculated. In particular, one right-symmetric central extension of $W_1^{rsym}$ is constructed.

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Askar Dzhumadil'daev. 1998-07-13. Cohomologies and deformations of right-symmetric algebras. https://arxiv.org/abs/math/9807065

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